Since the tenant has been paying you monthly lease rentals by cheques, it is sufficient proof that the tenant is in possession of the property.
The tenant is not correct in asking for 15 months time to vacate the premises and this is totally unreasonable and against law. .
The legal position in your case is as follows:
In absence of any lease agreement, it is construed in law, that it is a month on month lease. In effect it means that the tenant needs to vacate within a period of 15 days, if the notice has been served on him.
Section 106 in the transfer of property act refers to certain leases in absence of written contract. (Reproduced below).
Since the tenant has been using your building for last 9 years, the maximum time you can offer as a good will
gesture to your tenant is about 3 months to vacate the premises. Please note that i have recommended 3 months as a good will gesture and not 15 days notice for the reason that tenant cannot claim insufficient time for vacating a premises as 90 days is a good amount of time for finding alternate premises in eyes of law.
You should also keep all communications with your tenant in writing .
Section 106 in The Transfer of Property Act, 1882
1[106. Duration of certain leases in absence of written contract or local usage.—
(1) In the absence of a contract or local law or usage to the contrary, a lease of immovable property for agricultural or manufacturing purposes shall be deemed to be a lease from year to year, terminable, on the part of either lessor or lessee, by six months' notice; and a lease of immovable property for any other purpose shall be deemed to be a lease from month to month, terminable, on the part of either lessor or lessee, by fifteen days' notice.
(2) Notwithstanding anything contained in any other law for the time being in force, the period mentioned in sub-section (1) shall commence from the date of receipt of notice.
(3) A notice under sub-section (1) shall not be deemed to be invalid merely because the period mentioned therein falls short of the period specified under that sub-section, where a suit or proceeding is filed after the expiry of the period mentioned in that sub-section.
(4) Every notice under sub-section (1) must be in writing, signed by or on behalf of the person giving it, and either be sent by post to the party who is intended to be bound by it or be tendered or delivered personally to such party, or to one of his family or servants at his residence, or (if such tender or delivery is not practicable) affixed to a conspicuous part of the property.]